Problem: Reduce to lowest terms: $ \dfrac{5}{8} \div \dfrac{9}{7} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{9}{7}$ is $ \dfrac{7}{9}$ Therefore: $ \dfrac{5}{8} \div \dfrac{9}{7} = \dfrac{5}{8} \times \dfrac{7}{9} $ $ \phantom{ \dfrac{5}{8} \times \dfrac{7}{9}} = \dfrac{5 \times 7}{8 \times 9} $ $ \phantom{ \dfrac{5}{8} \times \dfrac{7}{9}} = \dfrac{35}{72} $